论文标题
按部分持续存在：通过分布式持续同源性检测多尺度功能
Persistence by Parts: Multiscale Feature Detection via Distributed Persistent Homology
论文作者
论文摘要
基于将广义的Mayer-Vietoris原理扩展到过滤空间的扩展，提出了一种持久同源性分布式计算的方法。细胞Cosheaves和光谱序列用于根据标量场索引的局部计算来计算全局持续的同源性。这些技术允许计算不仅是通过地理位置来定位的，还可以通过数据点的其他特征（例如密度）进行定位。作为后者的一个例子，该结构用于点云的多尺度分析中，以检测标准持续同源性忽略的不同大小的特征。
A method is presented for the distributed computation of persistent homology, based on an extension of the generalized Mayer-Vietoris principle to filtered spaces. Cellular cosheaves and spectral sequences are used to compute global persistent homology based on local computations indexed by a scalar field. These techniques permit computation localized not merely by geography, but by other features of data points, such as density. As an example of the latter, the construction is used in the multi-scale analysis of point clouds to detect features of varying sizes that are overlooked by standard persistent homology.
